Here is the full list of all 15 Don't Sink achievements.
Purchase the Man of War.
Complete a sea voyage that is at least 2,000 miles in distance.
Lost to the seas only you can find him. Rumor has it he is somewhere in the main menu!
Capture and own 6 islands at the same time.
Defeat 25 pirates at sea!
Capture an island!
Travel a total of 20,000 miles by sea.
Complete at least 50% of all available quests.
Spend 25,000 gold!
Build Cramton to completion starting from nothing.
Complete a sea voyage that is at least 1,000 miles in distance.
Complete the side quest, "Tough Decisions"
Try to capture the ferret captain!
Purchase a better ship.
Begin your journey!